Nonexistence of proper p-biharmonic maps and Liouville type theorems I: case of p≥2

2018/01/16 by Han, Yingbo, Luo, Yong
#Differential Geometry (math.DG) #FOS: Mathematics

paper · doi:10.48550/arxiv.1801.05181

Abstract

Let u: (M, g)→ (N, h) be a map between Riemannian manifolds (M, g) and (N, h). The p-bienergy of u is defined by E_p(u)=∫_M|τ(u)|^pdν_g, where τ(u) is the tension field of u and p>1. Critical points of E_p(⋅) are called p-biharmonic maps. In this paper we will prove nonexistence result of proper p-biharmonic maps when p≥2. In particular when M=ℝ^m, we get Liouville type results under proper integral conditions , which extend the related results of Baird, Fardoun and Ouakkas \citeBFO.

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